Question

Name the following triangle: `ΔQRS`, where `m∠R = 94, m∠Q = 22 and m∠S = 90`?

Answer 1

`DeltaQRS` is a spherical triangle.

Explanation:

Assuming that the angles of the triangle `DeltaQRS` are given in degrees, it is observed that

`m/_Q+m/_R+m/_S=22^@+94^@+90^@=206^@`.

As sum of the angles of the triangle is more than `180^@`, it is not a triangle drawn on a plane.

In fact it is on a sphere that sum of the angles of a triangle lies between `180^@` and `540^@`.

Hence `DeltaQRS` is a spherical triangle.

In such cases the amount by which it exceeds `180^@` (here `26^@`) is called spherical excess.